An introduction to geometric complexity theory
J.M. Landsberg
TL;DR
This paper introduces geometric complexity theory, a multidisciplinary approach combining differential geometry, algebraic geometry, and representation theory, to address the algebraic P vs NP problem through the permanent versus determinant challenge.
Contribution
It provides an overview of geometric complexity theory and its relevance to the algebraic P vs NP problem, integrating diverse mathematical methods.
Findings
Survey of geometric methods relevant to complexity theory
Connections between algebraic geometry and computational complexity
Framework for future research in algebraic complexity
Abstract
I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic analog of the P v. NP problem.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Graph Labeling and Dimension Problems